http:www.ugrad.cs.ubc.cacs314Vjan2005

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Textures IWeek 8, Mon Feb 28

• http//www.ugrad.cs.ubc.ca/cs314/Vjan2005

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News

• face to face p2 grading this week
• you can check your time slot from scans posted to
  course page
• (student numbers blocked out)
• Mon 1-5, Tue 10-1, 3-5, Wed 1-5
• midterm scaling announced

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Midterm 1 Raw Scores

• range 26-98, avg 66

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Midterm 1 Scaled Scores

• range 33-98, avg 69

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News

• Homework 2 Q1-3 correction
• point A is (2,0,0)
• point B is (3,0,0)
• point C is (4,0,0)

6
Review Warnocks Algorithm

• start with root viewport and list of all objects
• recursion
• clip objects to viewport
• if only 0 or 1 objects
• done
• else
• subdivide to new smaller viewports
• distribute objects to new viewpoints
• recurse

7
Review Warnocks Algorithm

• termination
• viewport is single pixel
• explicitly check for object occlusion
• single-pixel case common in high depth complexity
  scenes

8
Review Z-Buffer Algorithm

• augment color framebuffer with Z-buffer or depth
  buffer which stores Z value at each pixel
• at frame beginning, initialize all pixel depths
  to ?
• when rasterizing, interpolate depth (Z) across
  polygon
• check Z-buffer before storing pixel color in
  framebuffer and storing depth in Z-buffer
• dont write pixel if its Z value is more distant
  than the Z value already stored there

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Z-Buffer Demo
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Review Object vs. Image Space

• object space
• determine visibility on object or polygon level
• resolution independent, VCS / NDC coords
• early in pipeline
• requires depth sorting objects/polygons
• image space
• determine visibility at viewport or pixel level
• resolution dependent, screen coords
• late in pipeline

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Texturing
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Reading (whole week)

• FCG Chapter 10
• Red Book Chapter Texture Mapping

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Rendering Pipeline
Geometry Processing
Rasterization
Fragment Processing
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Texture Mapping

• real life objects nonuniform in terms of color
  normal
• to generate realistic objects - reproduce
  coloring normal variations Texture
• can often replace complex geometric details

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Texture Mapping

• introduced to increase realism
• lighting/shading models not enough
• hide geometric simplicity
• images convey illusion of geometry
• map a brick wall texture on a flat polygon
• create bumpy effect on surface
• associate 2D information with 3D surface
• point on surface corresponds to a point in
  texture
• paint image onto polygon

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Color Texture Mapping

• define color (RGB) for each point on object
  surface
• two approaches
• surface texture map
• volumetric texture

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Surface Texture

• define texture pattern over (u,v) domain (Image)
• image 2D array of texels
• assign (u,v) coordinates to each point on object
  surface
• for free-form use inverse of surface function
• for polygons (triangle)
• inside use barycentric coordinates
• for vertices need mapping function

v
u
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Texture Mapping


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Mapping for Triangular Meshes

• mapping defined by
• vertices (3D) mapped to specified (u,v) locations
  in 2D
• each interior point mapped to 2D using
  barycentric coordinates

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Texture Mapping

• texture map is an image, two-dimensional array of
  color values (texels)
• texels are specified by textures (u,v) space
• at each screen pixel, texel can be used to
  substitute a polygons surface property (color)
• we must map (u,v) space to polygons (s, t) space

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Example Texture Map
Applied to tilted polygon
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Texture Mapping

• (u,v) to (s,t) mapping can be explicitly set at
  vertices by storing texture coordinates with each
  vertex
• OpenGL
• generation at vertices
• specified by programmer or artist
• glTexCoord2f(s,t)
• glVertexf(x,y,z)
• ...

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Texture Coordinates

• every polygon has object coordinates and texture
  coordinates
• object coordinates describe where polygon
  vertices are on the screen
• texture coordinates describe texel coordinates of
  each vertex
• texture coordinates are interpolated along
  vertex-vertex edges
• glTexCoord1234sifd(TYPE coords)

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Example Texture Map
glVertex3d (s, s, s) glTexCoord2d(1,1)
glVertex3d (-s, -s, -s) glTexCoord2d(0,0)
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Example Texture Map
glVertex3d (s, s, s) glTexCoord2d(5, 5)
glVertex3d (s, s, s) glTexCoord2d(1, 1)
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Texture Lookup

• issue
• what happens to fragments with s or t outside the
  interval 01?
• multiple choices
• take only fractional part of texture coordinates
• cyclic repetition of texture to tile whole
  surfaceglTexParameteri( , GL_TEXTURE_WRAP_S,
  GL_REPEAT )
• clamp every component to range 01
• re-use color values from border of texture image
  glTexParameteri( , GL_TEXTURE_WRAP_S,
  GL_CLAMP )

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Texture Coordinate Transformation

• Motivation
• Change scale, orientation of texture on an object
• Approach
• texture matrix stack
• 4x4 matrix stack
• transforms specified (or generated) tex coords
• glMatrixMode( GL_TEXTURE )
• glLoadIdentity()

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Texture Coordinate Transformation

• Example

(0,1)
(1,1)
(0,0)
(1,0)
glScalef(4.0,4.0,?)
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Texture Functions

• once have value from the texture map, can
• directly use as surface color GL_REPLACE
• modulate surface color GL_MODULATE
• blend surface and texture colors GL_DECAL
• blend surface color with another GL_BLEND
• specific action depends on internal texture
  format
• only existing channels used
• specify with glTexEnvi(GL_TEXTURE_ENV,
  GL_TEXTURE_ENV_MODE, mode)

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Demo Robbins Tutor
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Texture Pipeline
Compute object space location
Use projector function to find (u, v)
Use corresponder function to find texels
Apply value transform function (e.g., scale, bias)
Modify illumination equation value
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Texture Pipeline
v
eye
Texel color (0.9,0.8,0.7)
u
(x, y, z) Object position (-2.3, 7.1, 17.7)
(u, v) Parameter space (0.32, 0.29)
Texture Image space (81, 74)
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Texture Mapping
t
(s2,t2)
1
(s0,t0)
(s1,t1)
0
s
0
1
(s, t) parameterization in OpenGL
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Texture Mapping

• texture coordinates
• generation at vertices
• specified by programmer or artist
• glTexCoord2f(s,t)
• glVertexf(x,y,z)
• generate as a function of vertex coords
• glTexGeni(), glTexGenfv()
• s ax by cz dh
• interpolated across triangle (like R,G,B,Z)
• well not quite!

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Texture Mapping

• texture coordinate interpolation
• perspective foreshortening problem
• also problematic for color interpolation, etc.

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Attribute Interpolation
Bilinear Interpolation Incorrect
Perspective correct Correct
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Texture Coordinate Interpolation

• perspective correct interpolation
• ?, ?, ?
• barycentric coordinates of a point P in a
  triangle
• s0, s1, s2
• texture coordinates of vertices
• w0, w1,w2
• homogeneous coordinates of vertices

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Volumetric Texture

• define texture pattern over 3D domain - 3D space
  containing the object
• texture function can be digitized or procedural
• for each point on object compute texture from
  point location in space
• common for natural material/irregular textures
  (stone, wood,etc)

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Volumetric Texture Principles

• 3D function r
• r r(x,y,z)
• texture space 3D space that holds the texture
  (discrete or continuous)
• rendering for each rendered point P(x,y,z)
  compute r(x,y,z)
• volumetric texture mapping function/space
  transformed with objects

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Texture Effects Simple Marble

• boring marble
• function boring_marble(point)
• x point.x
• return marble_color(sin(x))
• // marble_color maps scalars to colors

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Texture Effects Bombing

• bombing
• randomly drop bombs of various shapes, sizes and
  orientation into texture space (store data in
  table)
• for point P search table and determine if inside
  shape
• if so, color by shape
• otherwise, color by objects color